Engy 730 Assignment 1 April 04, 2021 This Assignment Is Mark

Engy 730 Assignment 1april 04 2021this Assignment Is Marked And W

This assignment involves analyzing historical data for a chiller within a building to develop and evaluate forecasting models for daily chilled water consumption. The key tasks include plotting data, applying various regression models (Simple Linear Regression, Second-Order Regression, and Multiple Linear Regression), generating forecasts for January 2014 based on varying weather parameters, and assessing model performance using metrics such as MAPE and RMSE. The assignment emphasizes understanding short-term/midterm forecasting concepts, feature extraction using regression models, and model justification based on fit quality.

Paper For Above instruction

Chiller performance optimization plays a significant role in reducing energy consumption in HVAC systems, which can account for approximately 70% of a building’s energy usage. Within this context, the efficiency of chillers, especially when producing chilled water for air conditioning, is critical. Improving the predictive accuracy of chilled water load forecasting enables better scheduling and operation optimizations, thus conserving energy and reducing operational costs. This paper discusses the development, application, and evaluation of regression-based models—specifically simple linear regression (SLR), second-order polynomial regression (SOR), and multiple linear regression (MLR)—applied to historical chilled water consumption data to forecast future loads with an emphasis on January 2014 predictions.

Introduction

The importance of precise load forecasting in building energy management systems cannot be overstated. Accurate forecasts allow for optimized chiller operations, leading to enhanced energy efficiency, cost savings, and environmental benefits. Given the considerable energy consumption associated with chillers, the focus on developing robust regression models is justified. Building on the understanding of thermodynamic processes and weather influences, this study leverages historical data to model daily chilled water demand based on key parameters, including Heating Degree Days (HDD), relative humidity (RH), and dew point temperature (Tdew-C).

Data Overview

The dataset encompasses daily measurements over a year, including variables such as chilled water usage in tons (chilledWater-TonDays), relative humidity (%), dew point temperature (Tdew-C), and Heating Degree Days (HDD). Visual analysis of the data reveals relationships between these variables—particularly, the inverse correlation between HDD and chilled water demand, as higher external temperatures typically reduce cooling loads, and vice versa. Additionally, the data exhibit seasonal patterns, trends, and potential outliers, which influence model development and accuracy.

Regression Models and Their Application

Simple Linear Regression (SLR)

The SLR model considers the relationship between one independent variable—HDD—and the dependent variable—daily chilled water consumption. The mathematical form is expressed as:

Chilled Water = β0 + β1 * HDD + ε

where β0 is the intercept, β1 is the slope coefficient, and ε is the error term. Plotting the data reveals a negative slope, consistent with the expectation that increasing HDD correlates with decreased cooling load. Regression analysis yields estimates for β0 and β1, which can be used to generate forecasted values for future dates.

Second-Order Regression (SOR)

The SOR model extends the simple regression to include a quadratic term to capture non-linear relationships:

Chilled Water = β0 + β1  HDD + β2  HDD^2 + ε

This model allows for curvature that might better fit the data, especially if the relationship between HDD and chilled water demand is non-linear. Regression fitting provides estimates for β0, β1, and β2, and the resulting equation can be used to forecast demand based on HDD inputs.

Model Development and Validation

Regression models are fitted using Excel or statistical software, with goodness-of-fit assessed via R-squared, residual analysis, and significance tests for coefficients. The models’ predictive capabilities are evaluated through cross-validation and visual comparison of observed versus predicted values. The models are then used to generate forecasts for January 2014, with the variations in HDD taken from the provided Table 1.

Forecasting Future Chilled Water Loads

Using the derived SLR and SOR models, forecasts for January 2014 are generated based on respective HDD values, assuming other weather variables are held constant or appropriately averaged. These predictions exemplify how temperature-related parameters affect cooling loads and enable planning for chiller operation schedules.

Multiple Linear Regression (MLR) and Its Application

The MLR model incorporates multiple influencing factors—HDD, RH, Tdew-C—thus providing a comprehensive understanding of their combined effect on chilled water demand. The model is expressed as:

Chilled Water = β0 + β1  HDD + β2  RH + β3 * Tdew-C + ε

The estimation process involves regression analysis to determine the coefficients, followed by validation through R-squared, residual diagnostics, and assessing multicollinearity among predictors. Once fitted, the MLR model offers improved predictive capacity by capturing the multifaceted factors impacting load variations. Forecasts for January 2014 are generated based on the designated parameters and their variability as per Table 1.

Model Evaluation

The accuracy of the models is quantitatively assessed using Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE). Lower values of these metrics indicate better fit and predictive performance. Comparative analysis demonstrates the trade-offs between simplicity and accuracy among SLR, SOR, and MLR models. Generally, inclusion of multiple variables and non-linear terms enhances the model, but also increases complexity and potential overfitting risks.

Discussion and Conclusions

The analysis indicates that the second-order regression provides a more accurate fit over the simple linear model due to its ability to model non-linear relationships. The MLR model further improves forecasting precision by considering additional weather parameters. However, the model's complexity requires careful validation to avoid overfitting and ensure robustness. Based on the evaluation metrics, the MLR model often exhibits the lowest RMSE and MAPE, suggesting its superiority for short-term load forecasting.

Implementing these models allows building operators to anticipate chilled water demands accurately, optimize chiller operations, and reduce energy consumption. The study underlines the importance of selecting appropriate models based on data characteristics and forecasting objectives, with a balanced consideration of complexity, interpretability, and accuracy.

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